The boundary fluctuation theory of transport coefficients in the linear-response limit

In this paper we present, for the first time, a linear-response theory of transport coefficients-shear viscosity and thermal conductivity-involving thermal, as opposed to mechanical, fields. The theory involves the explicit treatment of the boundaries and the constraints that are applied to them. Expressions for the shear viscosity and thermal conductivity are obtained in terms of the fluctuations at the boundaries of the variable conjugate to that which is constrained. We explain how the choice of ensemble, as defined by the boundary constraints, determines the form in which the transport coefficients are evaluated.